Process and system for determining correlation of public and private markets and risk of private markets

ABSTRACT

Process and system for investing in private portfolio includes determining relative risk, excess return and correlation of a private investment portfolio to a public market.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims benefit of U.S. Provisional ApplicationNo. 60/269,265, filed Feb. 15, 2001.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENTBACKGROUND OF THE INVENTION

[0002] Correlation

[0003] Publications pertaining to the correlation of the public andprivate markets have used the traditional method of computingcorrelation: plotting a series of index values RM (e.g., the return tothe S&P 500 index, the Wilshire 5000 index, the NASDAQ composite, etc.)on the x axis and corresponding stock or portfolio values R_(s) on the yaxis, with each pair representing returns for the same time period(daily, monthly, quarterly, annual, etc.). Least squares linearregression of these time series value pairs results in a so-calledcharacteristic line in the form:

R _(s)=α_(s)β_(S) R _(m) e _(s)

[0004] The β parameter of the characteristic line, when multiplied bythe market return, describes the systematic return of the stock orportfolio. Put another way, the β parameter describes the relativeriskiness of the investment, as defined by periodic volatility in thevalue of the stock or portfolio relative to the overall market. The e,parameter describes the unsystematic return, i.e., the company-specificor portfolio-specific risk of the stock or portfolio. The a parameter isthe y-intercept of the characteristic line, a constant that expressesthe stock or portfolio return associated with a market return of zero(the return expected if the market does not change).

[0005] Beta, the slope of the characteristic line, can also be describedin terms of the covariance of the stock and the market:$\beta_{s} = {\frac{{COV}_{sm}}{\sigma_{m}^{2}} = \frac{\sigma_{s}\sigma_{m}r_{sm}}{\sigma_{m}^{2}}}$

[0006] Solving for the correlation coefficient of the stock orportfolio, which is a measure of the percentage of movement in the stockor portfolio associated with the movement in the market, we obtain:$r_{sm} = \frac{\beta_{s}\sigma_{m}^{2}}{\sigma_{s}\sigma_{m}}$

[0007] When applied to stocks or portfolios of listed securities in thepublic markets, this method of estimating correlation works well. Whenapplied to the private markets, however, this method is inherentlybiased and inaccurate because the interim value of a private marketinvestment or portfolio (i.e., its value prior to realization) is, byits very nature as an illiquid asset, primarily an appraisal or estimateof value. Much as in the real estate market, values are sticky and thusappear to be less volatile (and therefore less risky) than they might beif an active market established values daily. Portfolio values in theprivate market are also affected by the j-curve phenomenon, in whichfees charged against constant portfolio values result in early negativereturns. Whether due to sticky values or the j-curve, the end result isan inaccurate determination of correlation.

[0008] For example, several correlation matrices, which include buyoutsand venture capital, as well as publicly traded stocks and bonds, arepublished annually in the Venture Economics Yearbook series. The 2000Yearbook, which covers private equity through Dec. 31, 1999, containsthe following data, reported in FIGS. 9.19 and 9.20. TABLE 1 CorrelationBased on Quarterly Returns for Longest Individual Series* Large SmallCorp. T- T- Venture Buyouts Mezzanine Equity Stock Stock Bonds BillsBonds PVCI Venture 100.0% 8.9% 13.7% 82.9% 39.0% 48.7% −18.5% −20.2%−19.2% 47.8% Buyouts 100.0% 21.9% 60.1% 13.5% 9.7% −5.7% −2.7% −10.0%−7.3% Mezzanine 100.0% 27.3% 11.9% 21.6% −29.0% −22.4% −32.6% 5.6%Equity 100.0% 40.8% 46.5% −20.3% −21.3% −22.9% 32.2% Large Stock 100.0%77.7% 6.8% 1.3% 2.6% 56.6% Small Stock 100.0% −4.3% −19.6% −10.1% 46.2%Corp. Bonds 100.0% 9.7% 97.5% 23.8% T-Bills 100.0% 7.5% −11.5% T-Bonds100.0% 17.2% PVCI 100.0% Beta 0.80 0.84 0.93 0.43 1.00 0.50 0.27 — 0.380.73

[0009] TABLE 2 Correlation Based on Annual Returns for Longest Series inCommon** Large Small Corp. T- T- Venture Buyouts Mezzanine Equity StockStock Bonds Bills Bonds PVCI Venture 100.0% −0.9% −14.4% 89.1% 22.3%39.7% −42.4% −33.5% −38.0% 69.8% Buyouts 100.0% 42.6% 38.1% 20.4% 28.7%8.4% −8.3% 10.3% −11.0% Mezzanine 100.0% 6.7% 0.8% 8.0% 32.8% −9.3%39.2% −13.0% Equity 100.0% 27.4% 50.9% −42.4% −48.4% −36.1% 60.4% LargeStock 100.0% 62.6% 54.9% 6.1% 56.7% 53.6% Small Stock 100.0% 30.9%−34.2% 30.4% 57.7% Corp. Bonds 100.0% 40.8% 98.6% 5.7% T-Bills 100.0%32.8% 32.8% T-Bonds 100.0% 4.2% PVCI 100.0% Beta 0.91 0.82 0.93 0.711.00 0.55 0.32 — 0.41 0.78

[0010] These two correlation matrices were calculated using thetime-weighted rates of return of the securities they contain. Theyprobably understate the correlation of the private markets and thepublic markets (and of the private markets to each other), as discussedabove, because private market valuations stay relatively constant overfairly long periods of time (e.g., most private equity firms holdinvestments owned less than one year at cost, which is a constant) ordecline (because of the j-curve phenomenon), while the market's valuesrise and fall daily. As a result, correlations looked at over the shortrun appear to be low—over short time periods the private investmentvalue does not move much in sympathy with the public market, theindependent variable—which is why, in the correlation matrices shownabove, correlations are much higher over yearly periods (Table 2) thanthey are over quarterly periods (Table 1).

[0011] The best way to remedy these deficiencies of the conventionalcorrelation computation would be to match private market and publicmarket investment outcomes over the same or very similar periods oftime, in order to allow the movement of private market values to berealized and thus known with certainty. Realized values are not stickyvaluations or biased estimates. They are cash or liquid securities, andthus outcomes that are directly comparable to the liquid alternativesavailable in an index of listed securities.

[0012] Benchmark

[0013] The present inventors previously published the Index ComparisonMethod (“ICM”) and developed it into a performance diagnostic. Since itspublication, the ICM has been adopted by many of the largest and mostsophisticated U.S. and European institutional investors and majorconsulting firms. The ICM also appears in the Venture Economics annualsurvey as the BLNC measure (the LN is for Long-Nickels) (2000 InvestmentBenchmarks Report, Venture, Capital, Venture Economics, Jesse Reyes,Editor in Chief, FIGS. 9.21, 9.22, 9.23 and 9.24).

[0014] The ICM is calculated, in simple terms, by the following steps:

[0015] 1. Compute the internal rate of return of the private investmentportfolio,

[0016] Obtain private investment asset, vintage and/or overall portfolioactual returns by listing their cash flows in columns, each cash flowaccompanied by its date, using natural signs (i.e. cash inflows arepositive numbers and cash outflows are negative numbers).

[0017] The final cash flow for each investment is its value at thereport date (i.e. all valuations are assumed realized at the report dateunless they have in fact been realized at an earlier date).

[0018] Compute an IRR for the private investment asset, vintage and/oroverall portfolios using these cash flows.

[0019] 2. Compute the comparable total return to an index of publicstocks had the cash flows in 1. been invested in the index.

[0020] List all cash flows as above for actual portfolio returns, butwithout showing an ending value/cash flow.

[0021] Compute the ending value/cash flow as follows:

[0022] (a) Treat the first (negative) cash flow as having been investedin the relevant index.

[0023] (b) Using an end-of-period assumption, grow that cash flow overthe time between the first and second cash flow at the rates indicatedby the linked index.

[0024] (c) At the point of the next cash flow, grow the new net amount(i.e. the amount of the prior cash flow grown by the linked index returnplus the new cash flow) by the relevant linked index until the date ofthe next cash flow.

[0025] Note that the next cash flow could be a distribution from theprivate investment, which would be treated as a withdrawal from theindex investment. Thus the new net amount could be the amount of theprior cash flow grown by the linked index return minus the new cashflow.

[0026] (d) Repeat step (c) until the calculation arrives at the currentreport date.

[0027] (e) Compute the IRR of the investment using the portfolio valueat the current report date, as computed in steps (a)-(d), as the finalcash flow/valuation as in the actual portfolio return computation above.

[0028] The result is a dollar-weighted time-weighted rate of return tothe public index that is directly comparable to the IRR performance ofthe private investment.

[0029] The return to the public index represents the opportunity cost ofinvesting in the private markets. This opportunity cost concept can beviewed as a benchmark: if the opportunity cost is a positive number(i.e., R_(M)—R_(s)≧0 ), the private investment underperformed the publicmarket; if opportunity cost is a negative number (i.e., R_(M)—R_(s)≦0)mthe private investment outperformed the public market.

SUMMARY

[0030] The present disclosure may be described therefore as a system andprocess for evaluation of private market investments as a part of theinvestment procedure. The disclosed methods and systems includedetermining three values of the private investment, the excess return onthe private investment over the public market, the risk associated withthe return on the private investment relative to the public market andthe correlation of the private investment to the public market.

[0031] The disclosure may also be described as a process for determiningthe risk of a private investment portfolio relative to the publicmarket, the correlation of a private investment portfolio to the publicmarket and the excess return of a private market portfolio over thepublic market by the steps of:

[0032] (a) determining the internal rate of return of the privateinvestment portfolio;

[0033] (b) determining an index comparison return (ICM) for the privateinvestment portfolio;

[0034] (c) plotting the values of (a) and (b) as points in a scatterplot with (a) on the y-axis and (b) on the x-axis and applying leastsquares linear regression to the resulting plot to yield a linearequation in the form y=βx+α, where β is the slope of the regression lineand α is the point at which the regression line crosses the y axis, anda value for R², the coefficient of determination;

[0035] (d) determining the correlation of the private market portfoliowith the public market index by taking the square root of thecoefficient of determination determined in (c) to yield the coefficientof correlation r (also known in statistical literature as the Greekletter ρ);

[0036] (e) determining the risk of the private investment of theportfolio by reference to the risk of the public market portfolio bysolving the equation${\frac{\beta_{vc}\sigma_{{S\&}P}^{2}}{r_{{VC},{{S\&}P}}\sigma_{{S\&}P}} = \sigma_{VC}};{and}$

[0037] (f) determining the excess return of the private investmentportfolio over the public markets by reference to the a of the linearregression line.

[0038] The disclosed process may also be used to evaluate the return vs.risk of a private investment portfolio by calculating the Sharpe ratioand comparing the private investment Sharpe ratio to the Sharpe ratio ofan appropriate public market.

[0039] The disclosure further includes a system for evaluation privatemarket investments including a central processing unit or CPU(processor), which may be a main-frame computer connected to one or morework stations, or it may be a component of a personal computer that maybe a “stand alone” computer or it may be networked to other computersthrough a common server. The system also includes an input device suchas a keyboard in communication with the processor, at least one memorysource and software including instructions. The device may also includea display device such as a monitor in communication with the processor.

BRIEF DESCRIPTION OF THE DRAWING

[0040] The following drawing forms part of the present specification andare included to further demonstrate certain aspects of the presentinvention. The invention may be better understood by reference to one ormore of these drawings in combination with the detailed description ofspecific embodiments presented herein.

[0041]FIG. 1 is a graph showing the Venture Economics venture capitalvintages from 1980 through 1996.

DETAILED DESCRIPTION

[0042] The ICM-Based Opportunity Cost Rate of Return Plot Method

[0043] An aspect of the present disclosure is a novel analytical methodthat uses private market and public market returns, made comparable bythe ICM, to calculate the correlation of the private and public markets.This analytical method is referred to as the ICM-based opportunity costrate of return plot. Briefly, the analyst calculates one scatter plotgraph point for each investment in the study: the y axis (the dependentvariable) is the investment IRR; the x axis (the independent variable)is the ICM. Each ICM value is an unbiased estimate of the public marketreturn outcome that would have been generated by investing in the indexrather than in the private investment. In other words, each ICM valuerepresents the public market opportunity cost of the related privateinvestment IRR.

[0044] Analogous to the discussion above, least squares linearregression on IRR/ICM scatter point graph points results in acharacteristic line in the form:

R _(x)=α_(s)+β_(S) R _(m) +e _(s)

[0045] The coefficient of correlation can be expressed as:$r_{sm} = \frac{\beta_{s}\sigma_{m}^{2}}{\sigma_{s}\sigma_{m}}$

[0046] If private investment returns were perfectly correlated with thepublic markets, each IRR would be equal to its corresponding ICM. Theresult would be a 45° line beginning at the origin; β would equal 1 andα would equal zero.

[0047] An example of a graph as described is shown in FIG. 1.

[0048] This analysis in FIG. 1 shows that venture capital, as an assetclass, is actually much more highly correlated with the public marketthan the correlation matrices above might imply, with a high beta (1.99,or almost twice as volatile as the market) and a dismal alpha (−25.5%).Using the characteristic line developed in the least squares linearregression analysis above, the venture capital market could be expectedto deliver the following returns, given the market assumptions shown:Expected Forecasted S&P 500 Priv. Eq. 6.0% −13.6% 8.0% −9.6% 10.0% −5.7%12.0% — −1.7% 14.0% 2.3% 16.0% 6.3% 18.0% 10.2% 20.0% 14.2%

[0049] The overall venture capital market has in fact delivered thereturns shown in this table over the 80s and the first half of the 90s.The fast rise of Internet stocks distorted the figures considerably, butthe rapid decline experienced by that sector is tending to bring themarket back into line with the returns shown in the table.

[0050] The following examples show how to calculate the private marketportfolio sigma and Sharpe ratio (return per degree of risk), using theprivate market portfolio IRR/ICM plot linear regression results and thefollowing equation that incorporates these results, as well as knownparameters of a publicly investible index over various time periods.$\frac{\beta_{vc}\sigma_{{S\&}P}^{2}}{r_{{VC},{{S\&}P}}\sigma_{{S\&}P}} = \sigma_{VC}$

TABLE 3 S&P 500 arithmetic mean 1926-1987*** 12.0% S&P 500 sigma 21.1%Sharpe ratio 0.57 y = βx + α Calc β α R² return σ_(vc) Sharpe Leastsquares 0.032 0.1912 0.0007 0.19504 25.5% 0.76 regression of ICM/IRR

[0051] TABLE 4 S&P 500 Arithmetic mean 1926-2000 13.0% S&P 500 sigma20.2% Sharpe ratio 0.64 y = βx + α Calc β α R² return σ_(vc) SharpeLeast squares 0.032 0.1912 0.0007 0.2 24.4% 0.80 regression of ICM/IRR

[0052] TABLE 5 S&P 500 Arithmetic mean 1988-2000 17.6% S&P 500 sigma15.1% Sharpe ratio 1.17 y = βx + α Calc β α R² return σ_(vc) SharpeLeast squares 0.032 0.1912 0.0007 0.2 18.2% 1.08 regression of ICM/IRR

[0053] These examples demonstrate the ability, based on the presentdisclosure, to compare the return vs. risk (Sharpe ratio) of a privateinvestment with the Sharpe ratio of a public index. Prior to the presentdisclosure, the inventors are unaware of any other method to evaluatethe comparative risk of a private investment portfolio. In other words,using the ICM computation one could have compared the returns of aprivate investment to a publicly traded index, but one could notevaluate the amount of risk that the investment represented compared tothe risk of investing in a stock index, for example.

[0054] Looking at the above examples, in Table 3, a private investmentis compared to the S&P 500 index for the years 1926-1987. As can be seenfrom the table, the return divided by risk was 0.57. In the privateinvestment, the return of about 19.5% was realized with less relativerisk than investing in the public index (a Sharpe ratio of 076). Theprivate investments also had a better Sharpe ratio than the publicmarket in Table 4, but were very slightly less in Table 5, when comparedto the S&P 500 for the years 1988-2000.

[0055] The present disclosure thus contains powerful and novel tools forthe evaluation of private investment risk versus the public markets,correlation with the public markets and excess return over the publicmarkets. These tools may be applied to portfolio management and/orinvestment selection decisions, including by not limited to assetallocation (how much of a portfolio to put into private investments);sub-asset allocation (how much of the private investment portfolioshould be in buyouts, venture capital, mezzanine, etc) and evaluationand/or pricing of private investment funds, private investment fundmanagers, funds of funds, funds of fund managers, portfolios of directinvestments, or secondary interests.

1. A process for quantifying risk, excess return and correlation of a private portfolio comprising, determining the risk of a private investment portfolio relative to the public market, the correlation of a private investment portfolio to the public market and the excess return of a private market portfolio over the public market by the steps of: (a) determining the internal rate of return of each investment in the private investment portfolio; (b) determining an index comparison return (ICM) for each investment in the private investment portfolio; (c) determining the private investment characteristics by plotting the values of (a) and (b) as points in a scatter plot with (a) on they-axis and (b) on the x-axis and applying least squares linear regression to the resulting plot to yield a linear equation in the form y =βx+α, where β is the slope of the regression line and α is the point at which the regression line crosses they axis, and a value for R², the coefficient of determination; (d) determining the correlation of the private market portfolio with the public market by taking the square root of the coefficient of determination determined in (c) to yield the coefficient of correlation r; (e) determining the risk (σ_(vc)) of the private market portfolio by reference to the risk of the public market by solving the equation ${\frac{\beta_{vc}\sigma_{{S\&}P}^{2}}{r_{{VC},{{S\&}P}}\sigma_{{S\&}P}} = \sigma_{VC}};$

(f) determining the excess return of the private investment portfolio over the public markets by reference to the a of the linear regression line; and (g) thus quantifying risk, excess return and correlation of a private portfolio.
 2. The process of claim 1, further including determining the Sharpe ratio of the private investment portfolio and comparing the Sharpe ratio of the private portfolio to the Sharpe ratio of a public market.
 3. The process of claim 1, wherein said process includes application of quantified risk, excess return and correlation of a private portfolio to management of an investment portfolio.
 4. The process of claim 1, wherein said process includes application of quantified risk, excess return and correlation of a private portfolio to selection of one or more investments.
 5. The process of claim 1, wherein said process includes application of quantified risk, excess return and correlation of a private portfolio to asset allocation into a private investment.
 6. The process of claim 1, wherein said process includes application of quantified risk, excess return and correlation of a private portfolio to sub-asset allocation within a private investment portfolio.
 7. The process of claim 1, wherein said process includes application of quantified risk, excess return and correlation of a private portfolio to pricing of private investment funds.
 8. The process of claim 1, wherein said process includes application of quantified risk, excess return and correlation of a private portfolio to evaluation of private investment funds.
 9. The process of claim 1, wherein said process includes application of quantified risk, excess return and correlation of a private portfolio to evaluation of a private investment fund manager.
 10. The process of claim 1, wherein said process includes application of quantified risk, excess return and correlation of a private portfolio to evaluation of funds of funds.
 11. The process of claim 1, wherein said process includes application of quantified risk, excess return and correlation of a private portfolio to evaluation of a fund of fund managers.
 12. The process of claim 1, wherein said process includes application of quantified risk, excess return and correlation of a private portfolio to evaluation of a portfolio of direct investments.
 13. The process of claim 1, wherein said process includes application of quantified risk, excess return and correlation of a private portfolio to evaluation of secondary interests.
 14. A system for investing in a private investment portfolio comprising, means for determining the risk of a private investment portfolio relative to the public market, the correlation of a private investment portfolio to the public market and the excess return of a private market portfolio over the public market comprising: (a) electronic means for determining the internal rate of return of the private investment portfolio; (b) electronic means for determining an index comparison return (ICM) for the private investment portfolio; (c) electronic means for determining the private investment characteristics by plotting the values of (a) and (b) as points in a scatter plot with (a) on the y-axis and (b) on the x-axis and electronic means for applying least squares linear regression to the resulting plot to yield a linear equation in the form y=βx+α, where β is the slope of the regression line and α is the point at which the regression line crosses the y axis, and a value for R², the coefficient of determination; (d) electronic means for determining the correlation of the private market portfolio with the public market by taking the square root of the coefficient of determination determined in (c) to yield the coefficient of correlation r; (e) electronic means for determining the risk (σ_(vc)) of the private market portfolio by reference to the risk of the public market by solving the equation ${\frac{\beta_{vc}\sigma_{{S\&}P}^{2}}{r_{{VC},{{S\&}P}}\sigma_{{S\&}P}} = \sigma_{VC}};$

(f) electronic means for determining the excess return of the private investment portfolio over the public markets by reference to the a of the linear regression line; and (g) electronic means for quantifying risk, excess return and correlation of a private portfolio.
 15. A process for quantifying risk, excess return and correlation of a private portfolio by analyzing the investment outcomes of the private investment portfolio, said process comprising, determining the risk of a private investment portfolio relative to the public market, the correlation of a private investment portfolio to the public market and the excess return of a private market portfolio over the public market by the steps of: (a) determining the internal rate of return of each investment in the private investment portfolio; (b) determining an index comparison return (ICM) for each investment in the private investment portfolio; (c) determining the private investment characteristics by plotting the values of (a) and (b) as points in a scatter plot with (a) on the y-axis and (b) on the x-axis and applying least squares linear regression to the resulting plot to yield a linear equation in the form y =β+α, where β is the slope of the regression line and α is the point at which the regression line crosses they axis, and a value for R², the coefficient of determination; (d) determining the correlation of the private market portfolio with the public market by taking the square root of the coefficient of determination determined in (c) to yield the coefficient of correlation r; (e) determining the risk (σ_(vc)) of the private market portfolio by reference to the risk of the public market by solving the equation ${\frac{\beta_{vc}\sigma_{{S\&}P}^{2}}{r_{{VC},{{S\&}P}}\sigma_{{S\&}P}} = \sigma_{VC}};$

(f) determining the excess return of the private investment portfolio over the public markets by reference to the a of the linear regression line; and (g) thus quantifying risk, excess return and correlation of a private portfolio. 